Solve ax^2-x+1=0

$$a x ^ { 2 } - x + 1 = 0$$

Solve for a

$$a=\frac{x-1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add x to both sides. Anything plus zero gives itself.

$$ax^{2}+1=x$$

Subtract 1 from both sides.

$$ax^{2}=x-1$$

The equation is in standard form.

$$x^{2}a=x-1$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{x-1}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{x-1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1-4a}+1}{2a}\text{; }x=\frac{-\sqrt{1-4a}+1}{2a}\text{, }&a\neq 0\\x=1\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1-4a}+1}{2a}\text{; }x=\frac{-\sqrt{1-4a}+1}{2a}\text{, }&a\neq 0\text{ and }a\leq \frac{1}{4}\\x=1\text{, }&a=0\end{matrix}\right.$$